There is a large variety of concepts used to generalize the classical Prandtl-Reuss relations of infinitesimal elasto-plasticity to finite strains. In this work, some basic approaches are compared in a qualitative way with respect to a certain invariance property. These basic approaches include the additive hypoelasto-plasticity with corotational stress rates, additive plasticity in the logarithmic strain space, and multiplicative hyperelasto-plasticity.The notion of weak invariance is introduced in this study. Roughly speaking, a material model is weakly invariant under a certain transformation of the local reference configuration if this reference change can be neutralized by a suitable transformation of initial conditions, leaving the remaining constitutive relations intact. We analyse the basic models in order to find out if they are weakly invariant under arbitrary volume-preserving transformations of the reference configuration.It is shown that the weak invariance property corresponds to a generalized symmetry which provides insights into underlying constitutive assumptions. This property can be used for a systematic study of different frameworks of finite strain elasto-plasticity. In particular, it can be used as a classification criterion.Keywords: finite strain elasto-plasticity, reference change, weak invariance, hypoelasto-plasticity, logarithmic elasto-plasticity, multiplicative plasticity 2000 MSC: 74D10, 74C15 determinant of a second-rank tensor X unimodular part of a second-rank tensor X T transposition of a second-rank tensor sym(X) symmetric part of a second-rank tensor skew(X) skew-symmetric part of a second-rank tensor tr(X) trace of a second-rank tensor X Frobenius norm of a second-rank tensor X : Y scalar product of two second-rank tensors t, t ′ , t 0 time instances (typically t 0 ≤ t ′ ≤ t) Z 0 initial state

We consider the numerical treatment of one of the most popular finite strain models of the viscoelastic Maxwell body. This model is based on the multiplicative decomposition of the deformation gradient, combined with Neo-Hookean hyperelastic relations between stresses and elastic strains. The evolution equation is six dimensional. For the corresponding local initial value problem, a fully implicit integration procedure is considered, and a simple explicit update formula is derived. Thus, no local iterative procedure is required, which makes the numerical scheme more robust and efficient. The resulting integration algorithm is unconditionally stable and first order accurate. The incompressibility constraint of the inelastic flow is exactly preserved. A rigorous proof of the symmetry of the consistent tangent operator is provided. Moreover, some properties of the numerical solution, like invariance under the change of the reference configuration and positive energy dissipation within a time step, are discussed. Numerical tests show that, in terms of accuracy, the proposed integration algorithm is equivalent to the classical implicit scheme based on the exponential mapping. Finally, in order to check the stability of the algorithm numerically, a representative initial boundary value problem involving finite viscoelastic deformations is considered. An FEM solution of the representative problem using MSC.MARC is presented.

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The concept of representative directions is intended to generalize one‐dimensional material models for uniaxial tension to complete three‐dimensional constitutive models for the finite element method. The concept is applicable to any model which is able to describe uniaxial loadings, even to those for inelastic material behavior without knowing the free energy. The typical characteristics of the respected material class are generalized in a remarkable similarity to the input model. The algorithm has already been implemented into the finite element systems ABAQUS and MSC.MARC considering several methods to increase the numerical efficiency. The implementation enables finite element simulations of inhomogeneous stress conditions within technical components, though the input model predicts uniaxial material behavior only.

This work deals with the modelling and simulation of curing phenomena in adhesively bonded piezo metal composites which consist of an adhesive layer with integrated piezoelectric module and two surrounding metal sheet layers. In a first step, a general modelling framework is proposed which is able to represent curing phenomena in polymers at finite strains. Based on this formulation, a concretized model is deduced for the simulation of curing in one specific epoxy based adhesive. Here, appropriate material functions are specified and the thermodynamic consistency is proved. Regarding the finite element implementation, a numerical integration scheme and a new approach for the consideration of different initial conditions are provided. Finally, finite element simulations of a newly proposed manufacturing process for the production of bonded piezo metal composite structures are conducted. A deep drawing process of the composite with uncured adhesive layer and the subsequent adhesive curing are investigated.Keywords bonded piezo metal composite · curing adhesive · constitutive model · finite element method